Delft University of Technology
Effect of single-side stroke limiter on cantilever-based piezoelectric energy harvesting
from low frequency vibrations
Giannopoulos, Dimosthenis; Chen, Yu Chen; Van Der Zwaag, Sybrand; Groen, Pim DOI
10.1088/1361-665X/abee36
Publication date 2021
Document Version Final published version Published in
Smart Materials and Structures
Citation (APA)
Giannopoulos, D., Chen, Y. C., Van Der Zwaag, S., & Groen, P. (2021). Effect of single-side stroke limiter on cantilever-based piezoelectric energy harvesting from low frequency vibrations. Smart Materials and Structures, 30(5), [055008]. https://doi.org/10.1088/1361-665X/abee36
Important note
To cite this publication, please use the final published version (if applicable). Please check the document version above.
Copyright
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy
Please contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim.
This work is downloaded from Delft University of Technology.
PAPER • OPEN ACCESS
Effect of single-side stroke limiter on cantilever-based piezoelectric
energy harvesting from low frequency vibrations
To cite this article: Dimosthenis Giannopoulos et al 2021 Smart Mater. Struct. 30 055008
Smart Materials and Structures Smart Mater. Struct. 30 (2021) 055008 (10pp) https://doi.org/10.1088/1361-665X/abee36
Effect of single-side stroke limiter on
cantilever-based piezoelectric energy
harvesting from low frequency
vibrations
Dimosthenis Giannopoulos
∗
, Yu-Chen Chen, Sybrand van der Zwaag
and Pim Groen
1Novel Aerospace Materials (NOVAM) group, Faculty of Aerospace Engineering, Technical University of Delft, Delft, The Netherlands
E-mail:D.Giannopoulos-1@tudelft.nl
Received 29 January 2021, revised 25 February 2021 Accepted for publication 12 March 2021
Published 1 April 2021
Abstract
Piezoelectric transducers which rely on oscillating cantilever-type beams to harvest mechanical energy locally available in environments have been of great interest as a substitute for batteries. Most of the research efforts focus mostly on designs which aim at resonance matching to achieve maximum energy output without taking the mechanical degradation of the piezoelectric layers into consideration. The purpose of this study is to propose an energy harvesting design which maximizes power output on the long run. Unimorph cantilevers, in which the neutral axis is located at the interface between the soft lead zirconium titanate (PZT) (PZT5A4) layer and the inert substrate (Pernifer 45), are used. An analytical model is developed to quantify the performance of the harvesters as a function of free length and tip mass. An experiment is set up to validate the theoretical model. To reduce the occurrence of cracks induced in the piezoelectric element due to the cyclic nature of the vibrational excitation, a housing acting as mechanical stroke limiter is adopted. The effect of the single-side stroke limiter on the power output and lifetime of the cantilevers is investigated. A 40 mm free length unimorph cantilever with 300 mg mass attached on the tip exhibiting an 18% increase in power output (0.1 mW) is proposed. An improved lifespan of the cantilevers is obtained by limiting the tensile deformation of the piezoelectric layer. This study opens the opportunity for more effective energy harvesting mainly through compressive operation for longer periods.
Keywords: energy harvesting, vibrations, single-side stroke limiter, bandwidth, electrical power, lifetime
(Some figures may appear in colour only in the online journal)
1
The author passed away during the preparation of the manuscript.
∗
Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of theCreative Commons Attribution 4.0 licence. Any fur-ther distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
1. Introduction
The increased demand for electronics, such as wireless sensors and health monitoring devices, in the coming era of the Inter-net of things (IoT) has raised urgent requirements for portable
and sustainable power [1,2]. Continuous advances in
elec-tronics technology allow the ongoing decreasing size of integ-rated circuits while batteries have not experienced the same rate of miniaturisation. Batteries, therefore, remain the largest
and heaviest component of the entire unit [3]. Furthermore, their limited lifespan and the necessity for periodic charging are a few more reasons that have led research efforts to
altern-ative power supplies [4,5]. Powering IoT devices using
para-sitic energy locally available in environments such as indus-trial machines, human body, structures, and vehicles has been an attractive solution. Environmental mechanical energy rep-resents one of the richest ambient sources. To scavenge this form of energy, electromagnetic induction, piezoelectricity and triboelectricity have been proposed as energy harvesting
approaches [6]. Among them, piezoelectricity is at the front of
scientific research due to its high energy density at low-scales,
ease of integration and miniaturization [7].
Cantilever-type energy harvesters with one or two active layers (unimorph or bimorph) located on a vibrating host struc-ture are the most utilized piezoelectric transducers which
gen-erate electrical energy from base excitations [8, 9]. Brittle
ceramics, such as lead zirconium titanate (PZT), are usually used as piezoelectric material due to their high
electromech-anical coupling coefficient [10]. Piezoelectric beams generate
significant energy output when they are excited at resonance
[11]. However, such harvesters are not effective when there
are small fluctuations in the ambient vibration frequency due
to their relatively narrow operational bandwidth [12]. With
regard to this issue, several approaches that allow frequency tuning have been proposed, such as monostable and bistable
[13–16], multi-cantilever structures [13], passive and active
stiffness-tuning technologies [17].
Most of the research efforts focus on optimising energy harvesters to achieve maximum energy output without taking
their long term stability into consideration [18]. Piezoelectric
energy harvesters are intended to replace batteries since they can theoretically offer power for unlimited time, thus mak-ing the lifetime one of the most essential properties to end users. However, one can notice that this issue has seldom been addressed in the literature. The cyclic nature of the vibrational excitation, the non-uniform strain distribution along the length of the beam and the addition of a large proof mass on the tip are some of the reasons that make the mechanical degradation
of the piezoelectric layers inevitable [19,20].
From the perspective of applications, the insufficient power output, narrow operational bandwidth, and limited lifetime due to cyclic fatigue are the main barriers that prevent cantilever-type energy harvesters from being widely adopted in engineering practice. In this paper, a unimorph cantilever-based energy harvesting design which addresses these three metrics simultaneously is reported. A single-side stroke lim-iter is adopted allowing asymmetric deflection. The influence of the resulting boundary conditions on the generated power at various distances between the stroke limiter and the beam, is explored. The resonance frequency of the unimorphs as a function of the free length and tip mass and the operational bandwidth through different impact stages are studied. The variation of the unimorphs lifetime is explored by limiting either the compressive or tensile bending movement and the results are compared. This study provides guidance in design-ing piezoelectric energy harvesters and opens the opportunity
for more effective energy harvesting for longer period mainly through compressive operation.
2. Experimental
2.1. Preparation of piezoelectric unimorphs
In this study, unimorph cantilevers were fabricated. Soft PZT (PZT-5A) with a Young’s modulus of 69 GPa was selected as piezoelectric material. Pernifer 45 with a Young’s modulus of 193 GPa and thermal expansion coefficient similar to the piezoelectric material was used as a passive substrate layer. The two layers were glued together using epoxy (302-3M) blended with 5 wt% nickel balls to create a conductive path
and then cured at 700◦C for 3 h. The thickness of the
adhes-ive layer was adjusted so that the neutral axis of the unim-orph was located at the interface between the active and the passive layer. A thin layer of carbon paste (DuPont 7102) act-ing as electrode was fabricated on the top of the PZT layer by doctor-blading. To induce the piezoelectric activity, the unim-orph cantilevers were subjected to contact poling where a high
electric potential of 500 V (2 kV mm−1) was applied in the
thickness direction for 10 min. The width and total thickness of the unimorphs were fixed at 5 and 0.45 mm, respectively. Three different free lengths were tested; 20, 30 and 40 mm. As for proof mass, steel foil attached at the free end of the can-tilever was used. The number of stacked pieces of steel foil defined the weight of the tip mass.
2.2. Harvester configuration
To reduce or even better to avoid the occurrence of cracks in the piezoelectric element due to large oscillations, a
stroke-limiting casing was adopted (figure1). The cases were made
of acrylonitrile butadiene styrene by 3D printing. The casing was designed to limit only the upwards bending movement of the unimorphs. When the unimorphs bend downwards, they are free to move. The dimensions of the casing were optim-ized depending on the estimated tip mass deflection under con-trolled non-resonant excitation conditions and the free length of the unimorph cantilevers. To study the effect of different strokes H, a screw (ISO metric, M3) located at the end of the case was used as stroke limiter. H is defined as the dis-tance between the bottom part of the stroke limiter and the upper surface of the unimorph cantilever or the tip mass when exists. The unimorph can be clamped such that the piezoelec-tric layer is the top or the bottom layer. The tip mass is always on top.
2.3. Measurements
Mechanical Analysis in bending mode was performed to estimate the maximum permissible deflection limit of the unimorphs as a function of the free length using the RSA-G2 Solids Analyzer. For the experiments, the single canti-lever measuring system was used where the specimens were clamped at one end and deformed at the free end. The bending
Smart Mater. Struct. 30 (2021) 055008 D Giannopoulos et al
Figure 1. Schematic drawing of the harvester placed inside the deflection-limiting casing. The unimorph can be inverted such that the piezoelectric layer is the bottom layer.
strength of 20 and 40 mm free length unimorphs was tested
under linear strain rate of 1 µm s−1at room temperature. To
estimate the ultimate compressive displacement of the PZT layer, the specimens were placed on the sample holder in such way that the PZT layer was the bottom layer and the sub-strate the top layer. The tensile behaviour was determined by reversing the direction of the stresses within the two layers (the samples were flipped).
A harmonic signal, generated from a function generator (Agilent 33210A) and regulated using a power amplifier (Brüel&Kjær, Type 2706), was used to drive an electro-dynamic shaker (Brüel&Kjær, Type 4809). To provide mech-anical excitation, the unimorph cantilevers were clamped on an electrodynamic shaker using a simple Perspex clamping setup. An accelerometer (Brüel&Kjær, Type 4384) mounted on the base of the vibration exciter, was used to measure the amplitude of the driving vibration. The accelerometer used
has sensitivity of 0.773 mV ms2. For given input conditions,
the output voltage of the energy harvesters was measured and recorded with an oscilloscope (Agilent DSO-X 2004A). Res-istance matching was performed by measuring the voltage
across various load resistances (Rload) embedded in a
resist-ance decay box. Finally, the data were collected using a
USB-NI 6008 National Instruments® data acquisition and
elabor-ated by LabVIEW.
The harvested power was calculated by the following
equation [17]: Prms= V2 rms Rload . (1)
The deflection at the tip of the unimorph cantilevers was measured using a Laser Doppler vibrometer (LDV; PSV-500, Polytec, Germany). For the performance of the experiments, the base excitation amplitude and frequency were fixed to 3.8 mm and 40 Hz, respectively. The results from this exper-iment were used to design the cases in such a way that they limit only the upwards bending movement of the unimorph cantilevers. To estimate the natural frequency of the unimorph
cantilevers with varied free length and proof mass, frequency sweep was performed and the output voltage was recorded using an oscilloscope. To determine the damping factor, the unimorph cantilevers were vibrated at resonance and then they were stopped abruptly. The damping factor of the unimorph cantilever was then calculated through the dynamic tip
dis-placement by the following equation [21]:
ζm= ln Ai Ai+1 r 4π2+ ln Ai Ai+1 2 (2)
where Aiand Ai+1the magnitude of displacement at two
con-secutive peaks in the decay curves.
The lifetime of the unimorph cantilevers with 40 mm free length was investigated. To shorten the testing time in the life-time testing, a higher frequency of 50 Hz was used and the tests were terminated after a maximum number of cycles (one day of continuous operation) had been reached. The base excita-tion amplitude was kept the same.
3. Analytical model
In this study, to estimate the tip deflection of the fabricated piezoelectric unimorph cantilevers, analytical modal analysis was performed for their linear transverse vibrations. The
canti-levers, shown in figure2, were modelled as undamped Euler–
Bernoulli beams with clamped–free boundary conditions and tip mass attached at the free end.
Using the Newtonian or the Hamiltonian approach, the gov-erning equation of motion for a uniform clamped-free Euler– Bernoulli beam subjected to harmonic excitation f (x, t) =
F (x) cos (ωt), can be written as [22–25]:
− EId2w (x, t)
dx2 + m
d2w (x, t)
dt2 = f (x, t) (3)
passive layer
active layer
F(x,t)
Figure 2. Unimorph cantilever subjected to distributed axial force per length.
where w(x,t) is the transverse displacement of the neutral axis (at point x and time t) due to bending, EI is the bending stiff-ness, and m is the mass per unit length of the beam. The
steady-state response can be expressed as [26]:
w (x, t) = ∞ X r=1 φr(x) ω2 r− ω2 Frcos ωt (4)
where φr(x) is the mass normalized Eigen function, r denotes
the rth vibration mode, ωrindicates the corresponding natural
frequency of the rth mode and ω the frequency of the vibration source.
For a fixed-free beam with mass attached at the free end, the nth-mode flexural resonance frequency is given by
[27,28]: fn= ωn 2π = 1 2π v u u u t 3EIL3 33/140m + Mt , (5)
where E the Young’s modulus, I the Moment of Inertia, m
the mass of the cantilever and Mtthe mass of the proof mass.
Consider a piezoelectric unimorph cantilever of length, L, and
width, w. The piezoelectric layer has a density, ρp, Young’s
modulus, Ep, and thickness, tp. The nonpiezoelectric stainless
steel layer has a density, ρs, Young’s modulus, Es, and
thick-ness, ts. Assuming that the thickness of the adhesive is small
enough to be neglected, the bending stiffness EI of the
unim-orph is then given by [28]:
EI = 12 W E2 pt4p+ E2st4s+ EpEStpts 4t2p+ 4t2s+ 6tpts (Eptp+ Ests) . (6) 4. Numerical model
In addition to the analytical studies, numerical approaches based on the finite element method software COMSOL Mul-tiphysics 5.4 have also been used to study the steady-state dynamics and electric response of the fabricated unimorph cantilevers. A 3D model, consisting of an active layer, a non-piezoelectric substrate made of Pernifer 45 and a proof mass at the free end of the cantilever (if exists), was built. The phys-ical and electrphys-ical properties of the selected materials are listed
in table1. In the actual unimorph harvester, an electrode was
deposited on the PZT side and an adhesive layer was used to bond the active and the passive layer. However, their influence on the analysis results can be ignored because their thicknesses are sufficiently thin compared to the other layers as to be neg-ligible. A fine-sized mesh based on tetrahedral elements (four nodes) was applied. Each node was characterized with trans-lations in the nodal x, y, and z directions, and electric potential
V (for piezoelectric elements). The cantilever was fixed at one
end and a sinusoidal body load in the z direction was applied along the beam length as a boundary load condition. To obtain the steady-state electrical response, a ground reference voltage was connected to the bottom surface of the PZT layer and an electrical circuit coupled together with an external load res-istor to the upper surface. Frequency domain and time depend-ent analysis were performed to estimate the natural frequency and stroke of the unimorphs as a function of free length and tip mass.
5. Results and discussion
5.1. Mechanical analysis
The load–displacement curves of 20 mm free length unim-orph cantilevers under quasi-static loading are presented in
figure 3(a). It can be observed that the ceramic can
with-stand more stresses in compression (where cracks appeared at approximately 3 mm deflection) than in tension (where cracks appeared at approximately 1 mm deflection). The results of this study are in good accordance with the literature which generally holds that ceramics are much more resistant to
com-pressive stress than tensile stress [18,29–31]. A unimorph
can-tilever with 40 mm free length was tested under same
con-ditions and the results are presented in figure 3(b). From an
analytical point of view, the stiffness decreases with increas-ing the free length. The slope in the load–displacement curve, which measures the extrinsic properties of the cantilever such
as the stiffness, decreases from 0.6 to 0.1 (N mm−1),
confirm-ing this. Furthermore, the values of ultimate displacement in both compression and tension appear deviations and this can be attributed either to the inhomogeneity of the materials or uncontrolled factors during the fabrication process of the uni-morph cantilevers.
Smart Mater. Struct. 30 (2021) 055008 D Giannopoulos et al
Table 1. Physical and electrical properties.
Density (kg m−3)
Young’s
modulus (MPa) Poisson’s ratio
Piezoelectric charge constant d33(pC N−1) Piezoelectric charge constant d31(pC N−1) PZT5A4 7900 69 0.35 460 195 Pernifer 45 8000 193 0.3 — — -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 ) N( ec r o F Displacement (mm)
Upwards-PZT under tension Upwards-PZT under tension Upwards-PZT under tension Upwards-PZT under tension Upwards-PZT under tension Downwards-PZT under compression
-4 -3 -2 -1 0 1 2 0.0 0.5 1.0 1.5 2.0 2.5 ] N[ ec r o F Displacement [mm] Upwards-PZT under tension Upwards-PZT under tension Upwards-PZT under tension Upwards-PZT under tension Downwards-PZT under compression Downwards-PZT under compression
a)
b)
Figure 3. Load–displacement curve of unimorph cantilever with free length (a) 20 mm and (b) 40 mm.
a)
b)
0 50 100 150 200 250 300 0 50 100 150 200 250 300 350 400 450 500 550 experimental data analytically (Eq. 5) Comsol )z H( nf yc n e u q er F Tip mass (mg) 20 mm free length 30 mm free length 40 mm free length 20 25 30 35 40 45 50 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 experimental data analytically (Eq. 4) ) m m( t n e m ec al psi D Free length (mm) 300 mg tip mass 200 mg tip mass 100 mg tip massFigure 4. Measured (a) tip deflection and (b) natural frequency as a function of free length and tip mass.
5.2. Tip deflection
The tip deflection as a function of free length and tip mass
was investigated and the results are presented in figure4(a).
As expected, the deflection of the tip increases by increasing either the length or the weight of the proof mass. Furthermore, we can notice that in all cases the deflection is less than the ultimate displacement found in the failure testing. This ensures that fatigue will be the reason for an unexpected mechanical failure and not the fact that the displacement of the unimorphs during operation exceeded the ultimate displacement.
To estimate the damping factor of the unimorphs, the res-onant frequency was determined and its variation by changing the length and the weight of the proof mass is depicted
in figure4(b). As expected, the scatter in the displacement
increases with increasing unimorph length but remains about 11% of the average deflection. The scatter in the resonant fre-quency was considerably smaller and was of the order of 2%. It can be seen that values of the natural frequencies from the ana-lytical results and numerical simulations using Comsol Mul-tiphysics have good agreement with the experimental data. For analytical calculations and numerical simulations an average value of 0.03 was used as damping factor.
5.3. Power output
Figure 5(a) shows the measured generated power at
differ-ent distances between the stroke limiter and the unimorph cantilever for 20, 30 and 40 mm free length unimorph
0.0 0.5 1.0 1.5 2.0 2.5 0 mg 100 mg 200 mg 300 mg ) W µ( t u pt u O r e w o P L=20mm 0 5 10 15 20 25 30 300 mg 200 mg 100 mg 0 mg ) W µ( t u pt u O r e w o P L=30mm -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0 20 40 60 80 100 stroke (mm) 300 mg 200 mg 100 mg 0 mg ) W µ( t u pt u O r e w o P L=40mm 0 200 400 600 800 1000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ) V( e d util p m A Frequency (Hz) 1.3 --> No contact 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ) V( e d util p m A 0.4 --> Contact 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ) V( e d util p m A -0.3 --> Double clamped
a)
c)
b)
0.00 0.05 0.10 0.15 0.20 -5 -4 -3 -2 -1 0 1 2 3 4 5 ) V( p-p V e g atl o V time (s) 0.00 0.05 0.10 0.15 0.20 -5 -4 -3 -2 -1 0 1 2 3 4 5 ) V( p-p V e g atl o V time (s) 0.00 0.05 0.10 0.15 0.20 -5 -4 -3 -2 -1 0 1 2 3 4 5 ) V( p-p V e g atl o V time (s)Figure 5. (a) Power output as a function of the stroke. Rectangle dots represent the ‘No contact’ region, star dots the ‘Contact’ region and circle dots the ‘Double clamped’ region, (b) Comsol model of a S-shape deformed cantilever; Von Mises stresses distributed along the length of the cantilever, (c) signal processing of the output voltage in the three regions using FFT.
cantilevers. For high values of H, there is no contact between the cantilever and the stroke limiter and therefore the power output remains stable. This is the so-called ‘No contact’ region. In this region, it is assumed that the cantilever vibrates according to the first mode shape (Mode 1) where all the stresses appear at the anchor. As the stroke H decreases, the cantilever hits the stroke limiter (contact region) and its dynamic behavior becomes highly non-linear. It can be
observed that the power output decreases and the reason for this trend is the limitation of the deformation which results in less stresses at the anchor. As the weight of the tip mass increases, larger transverse displacements are developed and the phenomenon of power reduction is more obvious. The negative values of H indicate that the cantilever is already deformed downwards by the stroke limiter before the vibra-tions start (double clamped region). As a result, the cantilever
Smart Mater. Struct. 30 (2021) 055008 D Giannopoulos et al 0 50 100 150 200 250 300 350 400 450 500 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 ] s/ m [ e d uti n g a M Frequency [ Hz ] No contact Contact Double clamped
Figure 6. Operational bandwidth for different regions.
deforms according to a different mode shape where stresses
are mostly developed in the middle of the beam [32]. In this
case, the deformation of the cantilever is significantly smal-ler and this explains the extremely low value of generated power.
As the free length of the cantilever increases, larger trans-verse displacements are developed making the three regions
more apparent. It can be observed from figure5(a), that the
trend of the generated power for longer cantilevers is not the same as for the 20 mm length cantilever. Specifically, small peaks appear at specific distances between the cantilever and the stroke limiter indicating that the energy harvester produces more power. According to previous studies, when the tip of the cantilever hits the stroke limiter, the mass center contin-ues moving upwards due to its inertia resulting in a large curvature in the middle of the beam. The S-shape deforma-tion where stresses appear not only at the anchor but along the
length of the beam is illustrated in figure5(b). A consequence
of this is that the PZT layer close to the clamped area is in compression while the remainder in tension and therefore the
positive charge is cancelled out by the negative charge [33,34].
This could be the reason for the decreased generated power after impact. However, it can be observed from the graphs that the power output increases at a specific stroke. After impact, the cantilever vibrates according to several modes, and stresses, possibly larger than that appeared at the anchor dur-ing the first mode, are developed. The positive influence of the stroke limiter on the generated power is in good
agree-ment with the work produced by Wang et al [35]. The same
phenomenon is not observed in the case of the 20 mm free length cantilever. It is assumed that, since the the 20 mm free length cantilever is more stiff, the S-shape due to impact does not appear and therefore the cantilever continuous vibrating according to the first mode. Since the displacement is limited because of the stroke limiter, the power output is less.
The combination of modes appearing due to the stroke limiter causes some of the parts of the cantilever to vibrate at higher frequencies. To further study this, signal analysis
using fast Fourier transformation (FFT) was performed in the generated voltage signals and the results are presented in
figure 5(c). One data point of each region from the power
output-stroke curve of the 40 mm free length unimorph canti-lever with 300 mg tip mass was selected for the analysis. The FFT reveals that the frequency content changes with the intro-duction of the stroke limiter. The electrical performance of the piezoelectric energy harvesters is frequency dependent. As the frequency of the vibration source is closer to the resonance fre-quency of the cantilever, the mechanical to electrical energy transduction is more effective. So the introduction of the high frequency movements results in an increased power output. The investigation of the energy gain at different frequencies exceeds the scope of this article.
5.4. Bandwidth
The effect of the mechanical stroke limiter on the operational bandwidth was also investigated. The laser vibrometer recor-ded the tip velocity of a 40 mm free length unimorph cantilever after performing frequency sweep and the results are
presen-ted in figure6. The stroke distances were selected according
to the data from figure5(a). From the figure, one can observe
that when there is no impact, the cantilever shows a sharp peak at approximately 130 Hz which is in good agreement with
figure 4(b). The introduction of the stroke limiter shifts the
center line of the resonance peak toward a higher frequency while preserving the same magnitude. Also, the operational bandwidth becomes wider which is beneficial for applica-tions where small fluctuaapplica-tions in the ambient vibration fre-quency are expected. In the case where the cantilever is already deformed downwards by the stroke limiter, it can be observed that the resonant frequency increases even more. Other studies have shown that the basic vibration frequency for the double-clamped beam is higher than that of the cantilever beam by a
factor of about 6.4 [36]. From the graph below, it can be seen
that the difference in the natural frequency is not so significant, fact that indicates that the cantilever does not deform accord-ing to the first mode of a double-clamped beam.
5.5. Lifetime
The operational lifetime of the unimorph cantilevers in
num-ber of cycles as a function of tip mass is shown in figure7(a).
As the weight of the tip mass decreases, the stresses developed at the achor are less and therefore the lifetime increases. For 320 mg tip mass, the unimorph cantilever failed after approx-imately 4 min (240 cycles). In all cases, the cracks developed close to the clamped zone.
To investigate the effect of the single-side deflection limit-ation on the lifetime, the unimorph cantilever with 320 mg tip mass was used as it was the most extreme case. The sample was initially placed in such way where the compressive dis-placement of the PZT layer was limited. When the unim-orphs bend downwards, the movement is impact-free. From
figure7(b), the positive influence of the stroke limiter on the
lifetime is clear. Pillatsch et al [18] obtained a similar
life-time trend when the deflection of a bimorph cantilever was
Figure 7. Operational lifetime vs (a) tip mass, (b) stroke. (c) Time dependent stroke of the cantilever using Comsol.
limited. To investigate the influence of the tensile stresses in the lifetime of the unimorphs, the PZT layer was placed as the bottom layer. A clear improvement in lifetime is obtained in the case where the tensile displacement of the PZT layer is limited by the stroke limiter. For low values of stroke, the uni-morphs can exceed one day of operation. To further investigate the difference in lifetime, the stroke was numerically estimated
and the results are shown in figure7(c). It can be observed that
the usage of a stroke limiter leads to an assymetric deflection. In the downwards bending movement, the unimorph deforms further than 0.2 mm and this is the reason for the difference
in the results in figure7(b). Furthermore, the high frequency
movements introduced due to the impact can not be captured in the steady-state dynamics response of the unimorph. The difference between the experimental results and the numer-ical simulations can be attributed to the inhomogeneity of the layers in the actual unimorph cantilever leading to different modes of deformation (e.g. torsion).
6. Conclusion
The adoption of the single-side stroke limiter has a pos-itive influence on the electrical and structural performance of a unimorph cantilever. In general, the generated power decreased along with a decrease in the deflection due to the
less strain levels. However, a small increase in the generated power was observed when the deflection was minimally con-strained and this trend seems to appear as the stiffness of the cantilever decreases. This can be unambiguously linked to the high frequency movements where the mechanical to electrical energy transduction becomes more effective. On the other hand, the lifetime was significantly improved, especially when the tensile displacement was limited. The structural and elec-trical performance of a unimorph cantilever can be improved when the tensile deflection of the ceramic layer is minimally constrained while keeping the deflection on the compressive side unconstrained. This study provides guidance in design-ing piezoelectric energy harvesters and opens the opportunity for more effective energy harvesting for longer period mainly through compressive operation.
Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).
Acknowledgments
During this project, Professor Groen tragically passed away. The remaining authors would like to thank him for his
Smart Mater. Struct. 30 (2021) 055008 D Giannopoulos et al
contribution in this and many other works. He was a valued colleague and friend, and he will be greatly missed. The authors would also like to thank Dr Andre Bossche and prof Dr Paddy French for their coordination of the work done in this study. This work is part of the research program Citius, Altius, Sanius with project number P16-28, which is financed by the Dutch Research Council (NWO).
ORCID iD
Dimosthenis Giannopoulos
https://orcid.org/0000-0002-0233-2266
References
[1] Shaikh F K and Zeadally S 2016 Energy harvesting in wireless sensor networks: a comprehensive review Renew. Sustain.
Energy Rev.55 1041–54
[2] Zhao C, Zhang Q, Zhang W, Du X, Zhang Y, Gong S, Ren K, Sun Q and Wang Z L 2019 Hybrid piezo/triboelectric nanogenerator for highly efficient and stable rotation energy harvesting Nano Energy57 440–9
[3] Niu S, Wang X, Yi F, Zhou Y S and Wang Z L 2015 A universal self-charging system driven by random biomechanical energy for sustainable operation of mobile electronics Nat. Commun.6 8975
[4] Safaei M, Sodano H A and Anton S R 2019 A review of energy harvesting using piezoelectric materials: state-of-the-art a decade later (2008–2018) Smart Mater.
Struct.28 113001
[5] Anton S R and Sodano H A 2007 A review of power
harvesting using piezoelectric materials (2003–2006) Smart
Mater. Struct.16 R1–R21
[6] Kim S G, Priya S and Kanno I 2012 Piezoelectric MEMS for energy harvesting MRS Bull.37 1039–50
[7] Yang Z, Zhou S, Zu J and Inman D 2018 High-performance piezoelectric energy harvesters and their applications Joule
2 642–97
[8] Priya S 2007 Advances in energy harvesting using low profile piezoelectric transducers J. Electroceram.
19 167–84
[9] Stuber V L, Deutz D B, Bennett J, Cannel D, De Leeuw D M, Van Der Zwaag S and Groen P 2019 Flexible lead-free piezoelectric composite materials for energy harvesting applications Energy Technol.7 177–85
[10] Deutz D B, Pascoe J-A, Schelen B, Van Der Zwaag S, De Leeuw D M and Groen P 2018 Analysis and experimental validation of the figure of merit for piezoelectric energy harvesters Mater. Horiz.5 444–53
[11] Sodano H A, Inman D J and Park G 2004 A review of power harvesting from vibration using piezoelectric materials
Shock Vib. Dig.36 197–205
[12] Liu H, Lee C, Kobayashi T, Tay C J and Quan C 2012 A new S-shaped MEMS PZT cantilever for energy harvesting from low frequency vibrations below 30 Hz Microsyst. Technol.
18 497–506
[13] Liu H, Lee C, Kobayashi T, Tay C J and Quan C 2012 Piezoelectric MEMS-based wideband energy harvesting systems using a frequency-up-conversion cantilever stopper
Sensors Actuators A186 242–8
[14] Fan K, Tan Q, Zhang Y, Liu S, Cai M and Zhu Y 2018 A monostable piezoelectric energy harvester for
broadband low-level excitations Appl. Phys. Lett.
112 123901
[15] Zhang H, Jiang S and He X 2017 Impact-based piezoelectric energy harvester for multidimensional, low-level, broadband, and low-frequency vibrations Appl. Phys. Lett.
110 223902
[16] Erturk A, Hoffmann J and Inman D J 2009 A
piezomagnetoelastic structure for broadband vibration energy harvesting Appl. Phys. Lett.94 254102
[17] Peddigari M, Lim K-W, Kim M, Park C H, Yoon W-H, Hwang G-T and Ryu J 2018 Effect of elastic modulus of cantilever beam on the performance of unimorph type piezoelectric energy harvester APL Mater.6 121107
[18] Pillatsch P, Xiao B L, Shashoua N, Gramling H M, Yeatman E M and Wright P K 2017 Degradation of bimorph piezoelectric bending beams in energy harvesting applications Smart Mater. Struct.26 035046
[19] Salazar R, Serrano M and Abdelkefi A 2020 Fatigue in piezoelectric ceramic vibrational energy harvesting: a review Appl. Energy270 115161
[20] Avvari P V, Yang Y and Soh C K 2017 Long-term fatigue behavior of a cantilever piezoelectric energy harvester
J. Intell. Mater. Syst. Struct.28 1188–210
[21] Huang H, Zheng C, Ruan X, Zeng J, Zheng L, Chen W and Li G 2014 Elastic and electric damping effects on piezoelectric cantilever energy harvesting Ferroelectrics
459 1–13
[22] Erturk A and Inman D J 2007 Mechanical considerations for modeling of vibration-based energy harvesters Volume 1:
21st Biennial Conf. on Mechanical Vibration and Noise,
Parts A, B, and C (ASMEDC) pp769–78
[23] Kim M, Hoegen M, Dugundji J and Wardle B L 2010 Modeling and experimental verification of proof mass effects on vibration energy harvester performance Smart
Mater. Struct.19 045023
[24] Erturk A and Inman D J 2008 A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters J. Vib. Acoust.130 041002
[25] Erturk A and Inman D J 2009 An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations Smart Mater. Struct.
18 025009
[26] Erturk A and Inman D J 2011 Piezoelectric Energy Harvesting (Chichester: Wiley) (https://doi.org/10.1002/
9781119991151)
[27] Dhakar L, Liu H, Tay F E H and Lee C 2013 A new energy harvester design for high power output at low frequencies
Sensors Actuators A199 344–52
[28] Yi J W, Shih W Y and Shih W H 2002 Effect of length, width, and mode on the mass detection sensitivity of piezoelectric unimorph cantilevers J. Appl. Phys.91 1680–6
[29] Roundy S, Leland E S, Baker J, Carleton E, Reilly E, Lai E, Otis B, Rabaey J M, Wright P K and Sundararajan V 2005 Improving power output for vibration-based energy scavengers IEEE Pervasive Comput.4 28–36
[30] Zhang T Y, Zhao M and Tong P 2002 Fracture of piezoelectric ceramics Adv. Appl. Mech.38 147–289
[31] Komai K, Minoshima K and Inoue S 1998 Fracture and fatigue behavior of single crystal silicon microelements and nanoscopic AFM damage evaluation Microsyst. Technol.
5 30–7
[32] Herrera-May A L, Aguilera-Cortés L A, García-Ramírez P J, Plascencia-Mora H and Torres-Cisneros M 2010 Modeling of the intrinsic stress effect on the resonant frequency of NEMS resonators integrated by beams with variable cross-section Microsyst. Technol.16 2067–74
[33] Clark W W and Mo C 2009 Piezoelectric energy harvesting for bio MEMS applications Energy Harvesting
Technologies ed S Priya and D J Inman (Boston, MA:
Springer US) pp405–30
[34] Wang Z, Elfrink R, Rovers M, Matova S, van Schaijk R and Renaud M 2014 Shock reliability of vacuum-packaged piezoelectric vibration harvester for automotive application
J. Microelectromech. Syst.23 539–48
[35] Wang F, Abedini A, Alghamdi T and Onsorynezhad S 2019 Bimodal approach of a frequency-up-conversion piezoelectric energy harvester Int. J. Struct. Stab. Dyn.
19 1950090
[36] Bao M-H 2000 Basic mechanics of beam and diaphragm structures Micro Mechanical Transducers: Pressure
Sensors, Accelerometers, and Gyroscopes (Hand Book of
